Question: Simplify the following expression: $ p = \dfrac{8x - 7}{-3x + 2} - \dfrac{-6}{7} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{8x - 7}{-3x + 2} \times \dfrac{7}{7} = \dfrac{56x - 49}{-21x + 14} $ Multiply the second expression by $\dfrac{-3x + 2}{-3x + 2}$ $ \dfrac{-6}{7} \times \dfrac{-3x + 2}{-3x + 2} = \dfrac{18x - 12}{-21x + 14} $ Therefore $ p = \dfrac{56x - 49}{-21x + 14} - \dfrac{18x - 12}{-21x + 14} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{56x - 49 - (18x - 12) }{-21x + 14} $ Distribute the negative sign: $p = \dfrac{56x - 49 - 18x + 12}{-21x + 14}$ $p = \dfrac{38x - 37}{-21x + 14}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{-38x + 37}{21x - 14}$